The public is split over the coalition government's plans for drastic cuts, according to the first poll conducted since Wednesday's comprehensive spending review.

The YouGov survey for the Sun reports 41% saying that the government's moves are good for the economy, 41% saying they are bad, and 18% saying they don't know.

But, asked if the cuts were too harsh or too cautious, 44% said too harsh, only 6% too cautious and 38% just right.

And asked if the spending reduction was being managed fairly or unfairly, 50% said unfairly while only 36% said fairly. In addition, 49% said the government was cutting too fast, against 4% who said it was too slow and 35% said about right.

A majority, 55%, said they agreed that "the government's plans to cut public spending amount to a desperate gamble with people's livelihoods" – one of Labour's key lines of attack.

However, the coalition government seems to have won the argument that cutting the deficit in this way is the only reasonable option available. The poll reports 58% saying the cuts are unavoidable, against 29% saying they are avoidable, something the shadow chancellor, Alan Johnson, has argued. In addition 47% blame the last Labour government for the cuts, against only 17% blaming the coalition.

Nick Clegg responded by calling the report "distorted and a complete nonsense". Ed Miliband, the Labour leader, said today: "Instead of trashing the Institute of [sic] Fiscal Studies, the deputy prime minister should be owning up to the truth. This was a spending review driven by ideology, hitting lower and middle income families the hardest. We have consistently warned about the consequences of cutting too far and too fast.

"The unedifying spectacle of Mr Clegg rubbishing the IFS will convince nobody of the government's case."

Today's YouGov figures for the state of the parties will make worrying reading for the Clegg and his party. While their coalition partners the Tories are on 41%, the Liberal Democrats are languishing on 10%, a fall of 13 points since the general election in May. Labour is snapping at the Conservatives' heels on 40%. Other parties were on 9%.

The poll found 40% approve of the coalition government, while 45% disapprove. Both of these figures had risen by one point since the spending review.

Other questions threw up some interesting answers. Asked whether the three party leaders were prepared to "take tough and unpopular decisions", 62% said this applied most to the Tories, with Labour and the Lib Dems managing only 10% and 5% respectively.

The Conservatives were most trusted to reduce the country's deficit (Con: 50%, Lab: 18%, Lib Dems: 3%), encourage economic growth (37:27:4), and, by a small margin, to cut spending in a fair and equal way (28:27:9).

YouGov also asked about specific policies. The proposal to remove child benefit from high-rate taxpayers – which caused fury in sections of the press and Tory party when it was announced at the Conservative conference – commands the support of 74% of those polled.

More people oppose (44%) than support (39%) the idea of cutting 490,000 public sector jobs.

Justice secretary Kenneth Clarke's policy of using community sentences instead of jail for some crimes is opposed by 60%, while allowing rail fares to rise faster than inflation is opposed by 80%.

Asked if the NHS, state schools, police forces and the BBC will get worse or better over the next few years, in every case more people said each service would get worse.